r Runoff - University of California, San...
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Convective Fluxes: Sensible and Latent
Heat
Convective Fluxes
• Convective fluxes require– Vertical gradient of temperature / water AND– Turbulence (‘mixing’)
• Vertical gradient, but no turbulence: only very slow diffusion of heat / water
• No vertical gradient, but turbulence: mixing, but no net transport of heat / water
Latent Heat Flux
z
humidity
Day & Night
Eddy = turbulent whirl Eddy moves warm humid air
up and dry air down. Bothmotions contribute to a positive (upward) flux of latent heat (“water flux”).
LE
Sensible Heat Flux
z
T
Day
Eddy moves warm air up and cold air down. Both motions contribute to a positive (upward) flux of sensible heat (“temperature flux”).
H
Sensible Heat Flux
z
T
Night
Eddy moves cold air up and warm air down. Both motions contribute to a negative (downward) flux of sensible heat (“temperature flux”).
H
Convective Fluxes` `
z
T
Sunrise/Sunset
H ?z
humidity
Moist air / Fog
LE ? Air saturated with water
vapor
Why is the lower atmosphere turbulent?
• Shear production of turbulence– Measured by shear stress or friction velocity
• Buoyant production / destruction of turbulence– Measured by sensible heat flux
• Obukhov length describes relative effect
2*
Uuz
' 'g w TT
3*
0.4 ' '
uL g w TT
L > 0 stable conditionsL < 0 unstable conditionsL = inf neutral conditions
Non-neutral boundary layers
• Unstable: – Large eddies– Deep atmospheric surface layer and
atmospheric boundary layer• Stable:
– Small eddies – Shallow surface layer
' ' 0w T
' ' 0w T
Neutral (‘wind tunnel’) Boundary Layer
Most simple and most investigated
Log layer (=constant flux layer):
dq/dz = E/(u* z rho k)
EC measurements make sense only above roughness sublayer and in the constant flux layer!
*
( ) lnm
u z du zk z
Stability correction functions for mean velocity profile
• Stability effects in the surface layer parameterized by Obukhov length L
3*
' '
uL m gk w TT
0 2 6 8 104 Wind speed [m s-1]
Hei
ght [
m]
.01
10
0.1
1
neutral
stable
unstable
*
( ) lnm
u z d zu zk z L
Hogstrom, 1988, Bound.-Layer Meteor.
Eddy Correlation3-d sonic anemometer
u’, v’, w’, Tv’ at 20 Hz
Krypton Hygrometerq’ at 20 Hz
Latent heat fluxSensible heat flux
' '
' '
w q
w T
Cup anemometer
sonic anemometer
Correlation and Fluxes
All atmospheric entities show short term fluctuations about their longer term mean. This is result of turbulence whichcauses eddies to continuously move and carry with them heat, vapor, momentum and other gases from elsewhere.
s s s s is value of an entity (T, vertical wind speed, vapor conc)s-bar is time-averaged entitys’ is instantaneous deviation from mean s-bar
Reynolds decomposition
Over a longer time period the value of the vertical wind speed w-barequals zero since mass continuity requires that as much air movesup as down during a certain period (eg 10-20 minutes).
The properties contained and transported by an eddy are its mass ρ(when considering a unit volume), its vertical velocity w, and thevolumetric content of any entity it possesses (heat, vapor, CO2).
Each of those components can be broken into a mean and a fluctuating part. Therefore, the mean vertical flux S of the entity s
/ ( )( )S ws w w s s
ws ws w s w s
All terms involving a single primed quantity are eliminated sincethe average of all their fluctuations equals zero by definition.
For uniform terrain without areas of preferred vertical motion(i.e. no “hotspots”) the mean vertical velocity (w-bar) equals zero.
S ws The averages of w’ and s’ are zero over a long enough time period.However, the average w’s’ which is the covariance of w’ and s’
will only rarely be negligible.
Transport of all entities depends on the vertical wind speedfluctuations.
covariance(w,s) ~ correlation coefficient (w,s) ~ vertical flux of s
Basic Statistics
Signal = mean + fluctuationse.g.
VariancesFluxes = covariance = w’T’
Correlation coefficient = covar. / variance
'u u u 22 2 1 1 2
1 1
' ( ) 'N N
ui i
u N u i u N u
1 1
1 1
' ' ( ) ( ) ' 'N N
i i
u w N u i u w i w N w u
1
1 ' '' 'N
uwiu w u w
w uw uN
(Oke, 1987)
Consider the following entities s: momentumtemperaturevapor concentration
Sensible heat flux H and latent heat flux E are measured as
' ' ' 'a p
v v v a
H c w T
E L w L w q
ρa: density of air [kg m-3] cp: specific heat of air [J kg-1 K-1]Lv: Latent heat of vaporization [J kg-1] ρv: water vapor density [kg H2O / m3 air]q: specific humidity [kg H2O / kg air]
If measurements can be made at least ten times per second, eddy covariance is an attractive method for directmeasurements of transport into the atmosphere.